The GUP implies a modification of the standard Heisenberg commutator, i.e., \([x_i,p_j]=i\hbar \delta _{ij}\) , by
terms induced from QG.
Although these terms imply significant contributions near the Planck length or energy scale, they give rise to potentially measurable effects at much lower energy scales.
A generalization of the GUP was proposed in Refs. [1]}, [2]}, [2]}, [4]}, [5]}, [6]}, [2]} of the form
\([x_i,\,p_j]=i\hbar \bigg [\delta _{ij}-&\alpha \bigg (p\,\delta _{ij}+\frac{p_ip_j}{p}\bigg )+\alpha ^2\bigg (p^2\,\delta _{ij}+3\,p_ip_j\bigg )\bigg ]\\[10pt]&[p_i,\,p_j]=[x_i,\,x_j]=0 ~.\) 
